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1 American Institute of Aeronautics and Astronautics
Aerodynamic Study of Airfoils with Leading Edge
Imperfections at Low Reynolds Number
Luis Ayuso*, Rodolfo Sant
† and José Meseguer
‡
Universidad Politécnica de Madrid, 28040 Madrid, Spain
A study has been made on the influence of the leading edge imperfections in airfoils used
in different devices relating their aerodynamic performances. Wind tunnel tests have been
made at different Reynolds numbers and angle of attacks in order to show this effect. Later,
a quantitative study of the aerodynamic properties has been made based on the different
leading edge imperfections and their size.
Nomenclature
CL = lift coefficient
CD = drag coefficient
CM = pitch moment
CP = pressure coefficient based on the freestream static and dynamics pressures
c = airfoil chord length, m
Re = Reynolds number
x = main chord direction, m
α = angle of attack, deg
∆x = upper displacement from the original leading edge, % c
I. Introduction
The§ interest of this study is based on the observation that some manufacturing processes produce imperfections
in the leading edge of some wings of various vehicles, wind turbine blades or other devices that use aerodynamic
profiles. Some manufacturing processes produce imperfections on the leading edge because they are manufactured
in two parts, top surface and bottom surface and subsequently joined. In this last process a sliding appears between
upper and lower surfaces causing a small displacement on the leading edge. Normally these imperfections are
corrected through a refill and sanding processes requiring many hours of manual labor.
Therefore the initial objective of this research is to determine the level of degradation in the aerodynamic
characteristics at low Reynolds numbers 1-6 of these imperfections in the manufacture, and determine whether there
may be a value for which it would not be necessary to correct them.
II. Experimental Setup
The experiments were performed in an open-circuit low-speed blow up wind tunnel in the Aerodynamics
Laboratory of the Aerotecnia Department at the Universidad Politecnica de Madrid. The wind tunnel has a test
section with a 1.2 by 0.16 m cross section and several windows, including an optically transparent one (Fig. 1). The
wind tunnel has a contraction section upstream of the test section, with screen structures to provide uniform low-
turbulent incoming flow to enter into the test section. Velocity distribution is <1% outside boundary layer and the
* Professor, Department of Aerotecnia/UPM,
and AIAA Member.
† Professor, Department of Aerotecnia/UPM.
‡ Principal Research Scientist, IDR/UPM.
40th Fluid Dynamics Conference and Exhibit28 June - 1 July 2010, Chicago, Illinois
AIAA 2010-4625
Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
2 American Institute of Aeronautics and Astronautics
mean turbulence level is < 0.5%. The air speed in test section can be steadily regulated for values from 5 to 30 m/s
and therefore test the airfoils up to 500,000 Reynolds numbers.
The airfoil used in the present study is a NACA0012 airfoil 7. Two models have been built for the tests, one of
them used for forces measurement with an electronic forces balance and for the use with laser anemometry, which
has a mechanism that allows you to scroll the upper on the lower surface according to graduations in % of chord.
The other model is also provided with 34 pressure taps at its median span (Fig. 2). Both models have been
manufactured in a numerical control milling machine using chemical wood, with great stability and a good surface
finish.
Model span is 15,6 cm, whereas that of the wind tunnel test chamber wide is 16 cm. No special provision has
been made to avoid the gap between model and wind tunnel walls, nor to correct measure results to take into account
this effect12, have been undertaken. It must be stressed that the aim of this work is to compare the aerodynamic
effect of different airfoil leading edge imperfections.
The models have a 24 cm chord, allowing test up to 450,000 Reynolds number with a of 30 m/s air velocity in
the test section.
Figure 2. NACA 0012 model. Airfoil model
fitted with pressure taps.
Figure 1. Wind tunnel scheme. Contraction,
test-section and diffuser configuration.
3 American Institute of Aeronautics and Astronautics
The forces have been measured through a 3 component electronic forces balance of PLINT Company, located in
one of the side walls of the test camera, which allows you to measure lift and drag forces, and pitch moment.
The pressure taps were connected to a pressure acquisition system (DSA3217, Scanivalve Corp.) for surface-
pressure measurements.
Laser-Doppler anemometry (LDA) measurements are in progress. It’s been performed with a DANTEC Flowlite
1D system. This system uses a 25mW Nd:YAG laser which produces green light ray of 1.35 mm diameter and
532nm. wavelength.
Models have been tested from -4º to 22° angles of attack, and Re = 150,000; 300,000 and 450,000. For each case
airfoils were studied with displacement of the upper on the lower surface of ±0.25%, ±0.5%, ±0.75% ±1.0% and
±1.5 %. Figure 3 shows the criteria of signs used to displacement ∆x, it is positive when the upper side moves
backward (positive sense the x-axis) and negative when it moves forward .
In all cases the following measures were made:
- Lift coefficient CL and drag coefficient CD , through the three components forces balance.
- Upper and lower surface pressure with scanivalve. - Boundary layer air speed with LDA (in progress).
III. Experimental Results
The experimental results are presented in the form of CL and CD versus angle of attack. Experiments show that at
the same Reynolds number small values of displacement (∆x) cause an increase in the maximum CL 8; for higher
values the trend is to have lower maximum CL values. If we study how the increase of the Reynolds number affects
the maximum CL, we will see that it increases with the Reynolds number and this happens in different proportions
for all studied displacements. At the same Reynolds number the CD increases slightly as the size of the displacement
increases. Looking at CD variance with the Re growth shows that minimum CD decreases for all displacements in
different magnitude. In any case, in this paper we’ll put the focus on analyzing the maximum lift coefficient of the
airfoil for the different displacements (∆x) tested.
Figure 4, 5 and 6 shows the effect of the displacement size on the lift coefficient at a fixed Reynolds number of
150,000; 300,000 and 450,000; and their influence on maximum CL values.
x
+∆∆∆∆x
Figure 3. Criterion of signs used for the displacement. ∆x positive when the upper side of the airfoil moves backward and negative when
moves forward.
x
-∆∆∆∆x
4 American Institute of Aeronautics and Astronautics
Figure 4. CL versus angle of attack. Re = 150,000. Effect of negative and positive displacement ∆x.
Figure 5. CL versus angle of attack. Re = 300,000. Effect of negative and positive displacement ∆x.
Re = 300.000
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
0 2 4 6 8 10 12 14 16 18 20 22
α
CL
0%
-0.25%
-0.5%
-0.75
-1%
-1.5%
Re = 150.000
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
0 2 4 6 8 10 12 14 16 18 20 22
α
CL
0%
-0.25%
-0.5%
-0.75
-1%
-1.5%
Re = 150.000
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
0 2 4 6 8 10 12 14 16 18 20 22
αC
L
0%
0.25%
0.5%
0.75
1%
1.5%
Re = 300.000
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
0 2 4 6 8 10 12 14 16 18 20 22
α
CL
0%
0.25%
0.5%
0.75
1%
1.5%
5 American Institute of Aeronautics and Astronautics
Figure 6. CL versus angle of attack. Re = 450,000. Effect of negative and positive displacement ∆x.
Figure 7, 8, 9 shows the effect of the displacement size on the drag coefficient at 150,000; 300,000 and 450,000
Reynolds number and their influence in CD values along the angle of attack range.
Figure 7. CD versus angle of attack. Re = 150,000. Effect of negative and positive displacement ∆x.
Re = 450.000
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
0 2 4 6 8 10 12 14 16 18 20 22
α
CL
0%
-0.25%
-0.5%
-0.75
-1%
-1.5%
Re = 450.000
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
0 2 4 6 8 10 12 14 16 18 20 22
α
CL
0%
0.25%
0.5%
0.75
1%
1.5%
Re = 150.000
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0 2 4 6 8 10 12 14 16 18 20 22
α
Cd
0%
-0.25%
-0.5%
-0.75
-1%
-1.5%
Re = 150.000
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0 2 4 6 8 10 12 14 16 18 20 22
α
Cd
0%
0.25%
0.5%
0.75
1%
1.5%
6 American Institute of Aeronautics and Astronautics
Figure 8. CD versus angle of attack. Re = 150,000. Effect of negative and positive displacement ∆x.
Figure 9. CD versus angle of attack. Re = 450,000. Effect of negative and positive displacement ∆x.
It must be pointed out that irrespective of the value of the Reynolds number, there are some leading edge
displacement (∆x) values which produce a noticeable growth of the lift coefficient (around some 5%). Although
such an increase depends on the Reynolds number, the maximum increase being reached at Re=3×105, where the lift
grows close to 20% when compared with nominal airfoil. Although these lift increments are not symmetrical with
respect to the sign of the displacement, the differences are not of significance except in the Re=3×105 case. Note
also that once the displacement is fixed, the lift coefficient increases and the drag coefficient decreases as the
Reynolds number grows, thus the airfoil efficiency increases with the Reynolds number. Such behaviour becomes
more subtle as the displacement increases, mainly when displacements are positive.
Re = 450.000
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0 2 4 6 8 10 12 14 16 18 20 22
α
Cd
0%
-0.25%
-0.5%
-0.75
-1%
-1.5%
Re = 450.000
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0 2 4 6 8 10 12 14 16 18 20 22
α
Cd
0%
0.25%
0.5%
0.75
1%
1.5%
Re = 300.000
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0 2 4 6 8 10 12 14 16 18 20 22
α
Cd
0%
-0.25%
-0.5%
-0.75
-1%
-1.5%
Re = 300.000
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0 2 4 6 8 10 12 14 16 18 20 22
α
Cd
0%
0.25%
0.5%
0.75
1%
1.5%
7 American Institute of Aeronautics and Astronautics
Those experiments carried out with pressure taps show a short laminar bubble. After laminar boundary layer
separates from the airfoil surface, the flow can reattach to the surface as a turbulent shear layer. This region between
the laminar separation and the reattachment is called a laminar separation bubble 9. The laminar separation bubble
on the airfoil is classified into a short bubble and a long bubble. With increasing angle of attack, the chordwise
length of the short bubble shortens and its position moves toward the leading edge. With further increase in the
angle of attack, the short bubble fails to reattach on the airfoil surface, which is known as a short bubble burst and
this bubble burst causes the airfoil stall. The long bubble, which is formed after the burst, increases its chordwise
length as the angle of attack is increased beyond the stall angle. The stall characteristics of the airfoil are strongly
dependent upon these two types of bubbles. The negative pressure peak near the leading edge is observed when the
short bubble is formed. When the long bubble is formed after the bubble burst, this negative pressure peak is
destroyed and a relatively flattened pressure distribution is formed (Fig. 10). Early investigations of the short bubble
mainly focused on predicting the short bubble burst 9–11
. Although the precise prediction of the short bubble burst
has not been accomplished, it was revealed that the laminar transition and turbulent flow inside the short bubble play
an important role in determining the short bubble burst.
Figure 10. Pressure coefficient in laminar separation bubble.
Separation and reattachment of short and long bubbles.
8 American Institute of Aeronautics and Astronautics
Pressure distributions along the airfoil chord for the nominal airfoil case (i.e., displacement ∆x = 0) and
Re=3x105 is show in Fig. 11 (these distributions correspond to angles of attack close to the stalling angle).
According to this plot, a laminar recirculation bubble appears at α = 10º, α = 12º and α = 13º (the short bubble is
formed when de angle of attack α is bellow 7 deg, see a high suction pressure near the leading edge followed by a
plateau area and a sudden pressure recovery). The bubble is shorter and closer to the leading edge as the angle of
attack increases (the leading edge suction peak increasing accordingly). At α = 14º the bubble shear layer can not
reattach and the airfoil stalls (note that at α = 16º the boundary layer is separated in the whole airfoil upper surface).
The results corresponding to displacement ∆x = -0.25 and ∆x = +0.25 are shown in Figs. 12a and 12b,
respectively, whereas those corresponding to ∆x = -0.50 and ∆x = +0.50 are depicted in Figs. 13a and 13b (these
plots correspond to the same nominal airfoil and the same Reynolds number and angles of attack already considered
in Fig. 11). As it can be observed in these cases experimental results reproduce the same behaviour as in Fig. 11.
Similar results are plotted in Fig. 14 and Fig. 15 for increasing values of the displacement ∆x. The main
difference as the displacement grows being the new boundary layer separation starts at the trailing edge.
Figure 11. Pressure coefficient. Cp distribution along the upper side of the
nominal airfoil. ∆x=0, Re=300,000 and angles of attack close to the stalling angle.
Re = 300.000 ∆∆∆∆x = 0%
-7
-6
-5
-4
-3
-2
-1
0
1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
x/c
CP
10 deg
12 deg
13 deg
14 deg
16 deg
9 American Institute of Aeronautics and Astronautics
Figure 13. Pressure coefficient. . Cp distribution along the upper side of the airfoil. Re=300,000 and
angles of attack close to the stalling angle. a) Displacement ∆x= -0.5%. b) Displacement ∆x= +0.5%.
a) b)
Re = 300.000 ∆∆∆∆x = - 0,5%
-7
-6
-5
-4
-3
-2
-1
0
1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
x/c
CP
10 deg
12 deg
13 deg
14 deg
16 deg
Re = 300.000 ∆∆∆∆x = +0,5%
-7
-6
-5
-4
-3
-2
-1
0
1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
x/c
CP
10 deg
12 deg
13 deg
14 deg
16 deg
Figure 12. Pressure coefficient. Cp distribution along the upper side of the airfoil. Re=300,000 and
angles of attack close to the stalling angle. a) Displacement ∆x=-0.25%. b) Displacement ∆x=+0.25%.
a) b)
Re = 300000 ∆∆∆∆x = -0.25%
-7
-6
-5
-4
-3
-2
-1
0
1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
x/c
CP
10 deg
12 deg
13 deg
14 deg
16 deg
Re = 300000 ∆∆∆∆x = 0.25%
-7
-6
-5
-4
-3
-2
-1
0
1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
x/c
CP
10 deg
12 deg
13 deg
14 deg
16 deg
10 American Institute of Aeronautics and Astronautics
Figure 15. Pressure coefficient. . Cp distribution along the upper side of the airfoil. Re=300,000 and
angles of attack close to the stalling angle. a) Displacement ∆x= -1.0%. b) Displacement ∆x= +1.0%.
a) b)
Re = 300.000 ∆∆∆∆x = +1%
-6
-5
-4
-3
-2
-1
0
1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
x/c
CP
10 deg
12 deg
13 deg
14 deg
16 deg
Re = 300.000 ∆∆∆∆x = - 1,0%
-6
-5
-4
-3
-2
-1
0
1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
x/c
CP
10 deg
12 deg
13 deg
14 deg
16 deg
Figure 14. Pressure coefficient. . Cp distribution along the upper side of the airfoil. Re=300,000 and
angles of attack close to the stalling angle. a) Displacement ∆x= -0.75%. b) Displacement ∆x=+0.75%.
a) b)
Re = 300.000 ∆∆∆∆x = -0,75%
-7
-6
-5
-4
-3
-2
-1
0
1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
x/c
CP
10 deg
12 deg
13 deg
14 deg
16 deg
Re = 300.000 ∆∆∆∆x = +0,75%
-7
-6
-5
-4
-3
-2
-1
0
1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
x/c
CP
10 deg
12 deg
13 deg
14 deg
16 deg
11 American Institute of Aeronautics and Astronautics
IV. Conclusion
Figures 16, 17 and 18 show the lift increasing for the different case of Reynolds number and displacement (∆x).
It is noticeable the increment of maximum lift coefficient when the displacement is small, and this occurs for all
case of Reynolds number studied.
The results show a degradation of the aerodynamic characteristics as the displacement size increases, bigger for
the highest values of studied Reynolds number. However, for certain combinations of low displacement size and
Reynolds number, aerodynamic performance seem to improve slightly. This suggests that they could limit values of
displacement that could be tolerated during manufacturing process, without that affecting considerably their
aerodynamic features.
Figure 17. Increment in maximum lift coefficient. Increment in maximum lift
coefficient (%) versus displacement ∆x, Re=300,000.
Re = 300.000
-40
-30
-20
-10
0
10
20
30
40
-1,50 -1,00 -0,50 0,00 0,50 1,00 1,50
∆x %
∆C
L m
ax .%
Figure 16. Increment in maximum lift coefficient. Increment in maximum lift
coefficient (%) versus displacement ∆x, Re=150,000.
Re = 150.000
-40
-30
-20
-10
0
10
20
30
40
-1,5 -1 -0,5 0 0,5 1 1,5
∆x %
∆C
L m
ax. %
12 American Institute of Aeronautics and Astronautics
References
1Lissaman, P.B.S., “Low–Reynolds-Number Airfoils,” Annual Review of Fluid Mechanics, Vol.15, Jan. 1983, pp. 223-239. 2Carmichael, B.H., “Low Reynolds Number Airfoil Survey”, Vol.1, NASA CR-165803, Nov. 1981. 3Nagamatsu, H.T., and Cuche, D.E., “Low Reynolds Number Aerodynamics Characteristics of Low-Drag NACA 63-208
Airfoil”, Journal of Aircraft, Vol.18, No.10, 1981, pp. 833—837. 4Schmitz, F.W., Aerodynamik des Flugmodells, Verlag, Duisburg, Germany, 1957. 5Cebeci, T., “Essential Ingredients of a Method for Low Reynolds Number Airfoils”, AIAA Journal, Vol.27, No.12, 1989, pp.
1680—1688.
6Mueller, T.J. and Batill, S.M., “Experimental Studies of Separation on a Two-Dimensional Airfoil at Low Reynolds
Number”, AIAA Journal, Vol.20, No.4, 1982, pp. 457—463. 7Abbott, I.H., and von Doenhoff, A.E., “Theory of Wing Sections”, Dover, New York, 1959. 8Jones, A.R., Bahktian, N.M. and Babinsky, H., “Low Reynolds Number Aerodynamics of Leading-Edge Flaps”, Journal of
Aircraft, Vol.45, No.1, 2008, pp.342—345. 9 Tani, I., Low-Speed Flows Involving Bubble Separation, Progress in Aeronautical Sciences, Pergamon Press, New York, Vol.
5, 1964, pp. 70–103. 10 Gault, D. E., “An Experimental Investigation of Regions of Separated Laminar Flow,” NACA TN-3505, 1955. 11Brendel, M., and Mueller, T. J., “Boundary-Layer Measurements on an Airfoil at Low Reynolds Numbers,” Journal of
Aircraft, Vol. 25, No. 7, 1988, pp. 612–617. 12Allen, H. J., and Vincenti, W. G., “Wall Interference in a Two-Dimensional-Flow Wind Tunnel, with Consideration of
compressibility,” NACA, Rept. 782, 1944.
Figure 18. Increment in maximum lift coefficient. Increment in maximum lift
coefficient (%) versus displacement ∆x, Re=450,000.
Re = 450.000
-40
-30
-20
-10
0
10
20
30
40
-1,5 -1,0 -0,5 0,0 0,5 1,0 1,5
∆x %
∆C
L m
ax.%
